The present invention relates to a process and an apparatus for measuring the biocurrent distribution and in particular to a process and an apparatus for indirectly determining the biocurrent distribution by measuring the biomagnetic field and estimating the distribution of the biocurrents which are sources of the magnetic field based upon the measured data.
Estimation of the biocurrent distribution from the measured values of the biomagnetic field is usually performed as follows:
Description will be made by way of a neuromagnetic measurement which is a typical biomagnetic field measurement.
The coordinate system is defined as shown in FIG. 1. It is assumed that a current represented as a vector q.sub.n exists at a position r.sub.n in the drawing. Such an isolated current vector can be assumed as far as the interface of the brain can be considered as a spherical surface in the field of neuromagnetic field measurement and this current vector will be referred to as a current dipole. A reference r.sub.m in FIG. 1 denotes the coordinate of the measuring point.
If it is assumed that N current dipoles exist in the brain, the magnetic flux density vector B.sub.m at point r.sub.m can be expressed from Biot-Savart's law as follows: ##EQU1##
The magnetic field component which can be measured by a magnetometer is the component of B.sub.m normal to the surface of the brain. The actual value measured at r.sub.m is denoted as D.sub.m.
If the estimated location and current vectors of each dipole are expressed by superscripting a reference mark , the virtual measured value D.sub.m which is calculated from the estimates is expressed as follows: ##EQU2## A cost function is herein defined as follows: ##EQU3##
Equation (3) shows the degree of matching between estimated data and actually measured data.
Optimum estimated values have heretofore been determined as r.sub.l , . . . , r.sub.N, . . . , q.sub.1, . . . , q.sub.N which minimize the cost function defined by the equation (3).
It is found from the foregoing that the number N of the biomagnetic field sources, that is, the current dipoles should be known in order to carry out the conventional measuring method. In other words, the conventional method can be carried out only if the number of the current dipoles is known.
If N which is different from the number of actual current dipoles is preset and a solution of r.sub.l, . . . , r.sub.N, q.sub.l, . . . , q.sub.N which minimizes the cost function is determined, the solution would then show a distribution different from the actual biocurrent distribution.